SOLUTION: The rodent population in our city is currently estimated at 30,000. If it grows at the rate of 8.5% per year, when will the population reach 100,000?use p= P0e^kt where p=populatio

Question 688083: The rodent population in our city is currently estimated at 30,000. If it grows at the rate of 8.5% per year, when will the population reach 100,000?use p= P0e^kt where p=population t=years
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
The rodent population in our city is currently estimated at 30,000. If it grows at the rate of 8.5% per year, when will the population reach 100,000?use p= P0e^kt where p=population t=years
.
first, we need to find the constant 'k'
do this using the info from:
" The rodent population in our city is currently estimated at 30,000. If it grows at the rate of 8.5% per year"
1.085(30000) = 30000e^(k*1)
1.085 = e^(k)
ln(1.085) = k
0.081579986992 =k
.
now, we can answer:
"when will the population reach 100,000?"
100000 = 30000e^(0.081579986992t)
10 = 3e^(0.081579986992t)
10/3 = e^(0.081579986992t)
ln(10/3) = 0.081579986992t
1.2039728043 = 0.081579986992t
1.2039728043/0.081579986992 = t
14.76 years = t

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